We present a fast, petaflop-scalable algorithm for Stokesian particulate flows. Our goal is the direct simulation of blood, which we model as a mixture of a Stokesian fluid (plasma) and red blood cells (RBCs). Directly simulating blood is a challenging multiscale, multiphysics problem. We report simulations with up to 200 million deformable RBCs. The largest simulation amounts to 90 billion unknowns in space. In terms of the number of cells, we improve the state-of-the art by several orders of magnitude: the previous largest simulation, at the same physical fidelity as ours, resolved the flow of O(1,000-10,000) RBCs. Our approach has three distinct characteristics: (1) we faithfully represent the physics of RBCs by using nonlinear solid mechanics to capture the deformations of each cell; (2) we accurately resolve the long-range, N-body, hydrodynamic interactions between RBCs (which are caused by the surrounding plasma); and (3) we allow for the highly non-uniform distribution of RBCs in space. The new method has been implemented in the software library MOBO (for “Moving Boundaries”). We designed MOBO to support parallelism at all levels, including inter-node distributed memory parallelism, intra-node shared memory parallelism, data parallelism (vectorization), and fine-grained multithreading for GPUs. We have implemented and optimized the majority of the computation kernels on both Intel/AMD x86 and NVidia's Tesla/Fermi platforms for single and double floating point precision. Overall, the code has scaled on 256 CPU-GPUs on the Teragrid's Lincoln cluster and on 200,000 AMD cores of the Oak Ridge national Laboratory's Jaguar PF system. In our largest simulation, we have achieved 0.7 Petaflops/s of sustained performance on Jaguar.

We present an inter-architectural comparison of single-and double-precision direct n-body implementations on modern multicore platforms, including those based on the Intel Nehalem and AMD Barcelona systems, the Sony-Toshiba-IBM PowerXCell/8i processor, and NVIDA Tesla C870 and C1060 GPU systems. We compare our implementations across platforms on a variety of proxy measures, including performance, coding complexity, and energy efficiency.

We present new scalable algorithms and a new implementation of our kernel-independent fast multipole method (Ying et al. ACM/IEEE SC '03), in which we employ both distributed memory parallelism (via MPI) and shared memory/streaming parallelism (via GPU acceleration) to rapidly evaluate two-body non-oscillatory potentials. On traditional CPU-only systems, our implementation scales well up to 30 billion unknowns on 65K cores (AMD/CRAY-based Kraken system at NSF/NICS) for highly non-uniform point distributions. On GPU-enabled systems, we achieve 30x speedup for problems of up to 256 million points on 256 GPUs (Lincoln at NSF/NCSA) over a comparable CPU-only based implementations.